Are the flexible sink tails/p-traps acceptable?
I just did the plumbing class. Flex pipe is not acceptable under the sink. According to the class. Expressed several times.
However they generally work fine and drain as intended.
And, I always recommend replacement due to clogging potential because they are not smooth on the inside nor are they up to current standards. 
I have also seen them split and crack over time. I always recommend replacement.
Plumbing Codes say drains are to be smooth bore, so we write them up.
We don’t make a BIG deal out of it but, we report them if present and recommend replacement.